The value of \(\Lambda \)  is fixed from \(A_s \approx 2.1\times 10^{-9}\) , where \(A_s\)  is the curvature power spectrum amplitude at the pivot scale \(k_* = 0.05 \; {\rm Mpc^{-1}}\)  [1]}.
Our numerical procedure is as follows. For a given parameter set we solve the background equations of motion, (REF ) and (), with the assumption that the inflaton starts to roll down the potential (REF ) near the origin; thus inflation takes place in the range \(0<\varphi <f\pi \) . The end of inflation is found by using the condition \(\epsilon _1 = 1\)  where \(\epsilon _1\)  is the first Hubble slow-roll parameter defined as Eq. (REF ). Choosing the number of e-folds of 70 for the pivot scale, we find the horizon-crossing time of the mode. We then solve the perturbation equations, (REF ) and (REF ), for a given wavenumber \(k\) . The initial conditions, (REF ) and (), are used when the mode is deep inside the horizon \(k\gg aH\) ; concretely we require \(k/(aH)\sim 10^{3}\) . We evolve the perturbation equations until the mode exits the horizon and resides far outside the horizon \(k\ll aH\) ; specifically we require \(k/(aH)\sim 10^{-3}\) . We then use Eqs. (REF ) and () to compute the power spectra. For Set 1 and Set 2, the curvature power spectrum (REF ) is shown in Fig. REF . As pointed out in Ref. [2]}, due to the ultra-slow-roll regime, we see a large enhancement in the curvature power spectrum.
Finally we compute the spectral index \(n_s\)  and the tensor-to-scalar ratio \(r\)  by using Eq. (REF ). They are given by \((n_s, r) = (0.96,0.079)\)  for Set 1 and \((0.96,0.080)\)  for Set 2.
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